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<h1 align="center">Source for file EigenvalueDecomposition.php</h1>
<p>Documentation is available at <a href="../JAMA/_PHPExcel---Shared---JAMA---EigenvalueDecomposition.php.html">EigenvalueDecomposition.php</a></p>
<div class="src-code">
<ol><li><div class="src-line"><a name="a1"></a><span class="src-php">&lt;?php</span></div></li>
<li><div class="src-line"><a name="a2"></a><span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a3"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@package</span><span class="src-doc">&nbsp;JAMA</span></div></li>
<li><div class="src-line"><a name="a4"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a5"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Class&nbsp;to&nbsp;obtain&nbsp;eigenvalues&nbsp;and&nbsp;eigenvectors&nbsp;of&nbsp;a&nbsp;real&nbsp;matrix.</span></div></li>
<li><div class="src-line"><a name="a6"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a7"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If&nbsp;A&nbsp;is&nbsp;symmetric,&nbsp;then&nbsp;A&nbsp;=&nbsp;V*D*V'&nbsp;where&nbsp;the&nbsp;eigenvalue&nbsp;matrix&nbsp;D</span></div></li>
<li><div class="src-line"><a name="a8"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;diagonal&nbsp;and&nbsp;the&nbsp;eigenvector&nbsp;matrix&nbsp;V&nbsp;is&nbsp;orthogonal&nbsp;(i.e.</span></div></li>
<li><div class="src-line"><a name="a9"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A&nbsp;=&nbsp;V.times(D.times(V.transpose()))&nbsp;and&nbsp;V.times(V.transpose())</span></div></li>
<li><div class="src-line"><a name="a10"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;equals&nbsp;the&nbsp;identity&nbsp;matrix).</span></div></li>
<li><div class="src-line"><a name="a11"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a12"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If&nbsp;A&nbsp;is&nbsp;not&nbsp;symmetric,&nbsp;then&nbsp;the&nbsp;eigenvalue&nbsp;matrix&nbsp;D&nbsp;is&nbsp;block&nbsp;diagonal</span></div></li>
<li><div class="src-line"><a name="a13"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;with&nbsp;the&nbsp;real&nbsp;eigenvalues&nbsp;in&nbsp;1-by-1&nbsp;blocks&nbsp;and&nbsp;any&nbsp;complex&nbsp;eigenvalues,</span></div></li>
<li><div class="src-line"><a name="a14"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;lambda&nbsp;+&nbsp;i*mu,&nbsp;in&nbsp;2-by-2&nbsp;blocks,&nbsp;[lambda,&nbsp;mu;&nbsp;-mu,&nbsp;lambda].&nbsp;&nbsp;The</span></div></li>
<li><div class="src-line"><a name="a15"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;columns&nbsp;of&nbsp;V&nbsp;represent&nbsp;the&nbsp;eigenvectors&nbsp;in&nbsp;the&nbsp;sense&nbsp;that&nbsp;A*V&nbsp;=&nbsp;V*D,</span></div></li>
<li><div class="src-line"><a name="a16"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;i.e.&nbsp;A.times(V)&nbsp;equals&nbsp;V.times(D).&nbsp;&nbsp;The&nbsp;matrix&nbsp;V&nbsp;may&nbsp;be&nbsp;badly</span></div></li>
<li><div class="src-line"><a name="a17"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;conditioned,&nbsp;or&nbsp;even&nbsp;singular,&nbsp;so&nbsp;the&nbsp;validity&nbsp;of&nbsp;the&nbsp;equation</span></div></li>
<li><div class="src-line"><a name="a18"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A&nbsp;=&nbsp;V*D*inverse(V)&nbsp;depends&nbsp;upon&nbsp;V.cond().</span></div></li>
<li><div class="src-line"><a name="a19"></a><span class="src-doc">&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a20"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@author</span><span class="src-doc">&nbsp;&nbsp;Paul&nbsp;Meagher</span></div></li>
<li><div class="src-line"><a name="a21"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@license</span><span class="src-doc">&nbsp;PHP&nbsp;v3.0</span></div></li>
<li><div class="src-line"><a name="a22"></a><span class="src-doc">&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@version</span><span class="src-doc">&nbsp;1.1</span></div></li>
<li><div class="src-line"><a name="a23"></a><span class="src-doc">&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a24"></a><span class="src-key">class&nbsp;</span><a href="../JAMA/EigenvalueDecomposition.html">EigenvalueDecomposition</a>&nbsp;<span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a25"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a26"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a27"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Row&nbsp;and&nbsp;column&nbsp;dimension&nbsp;(square&nbsp;matrix).</span></div></li>
<li><div class="src-line"><a name="a28"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">int&nbsp;</span></div></li>
<li><div class="src-line"><a name="a29"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a30"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a31"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a32"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a33"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Internal&nbsp;symmetry&nbsp;flag.</span></div></li>
<li><div class="src-line"><a name="a34"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">int&nbsp;</span></div></li>
<li><div class="src-line"><a name="a35"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a36"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$issymmetric</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a37"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a38"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a39"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Arrays&nbsp;for&nbsp;internal&nbsp;storage&nbsp;of&nbsp;eigenvalues.</span></div></li>
<li><div class="src-line"><a name="a40"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a41"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a42"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$d&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a43"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$e&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a44"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a45"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a46"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Array&nbsp;for&nbsp;internal&nbsp;storage&nbsp;of&nbsp;eigenvectors.</span></div></li>
<li><div class="src-line"><a name="a47"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a48"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a49"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$V&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a50"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a51"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a52"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Array&nbsp;for&nbsp;internal&nbsp;storage&nbsp;of&nbsp;nonsymmetric&nbsp;Hessenberg&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a53"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a54"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a55"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$H&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a56"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a57"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a58"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Working&nbsp;storage&nbsp;for&nbsp;nonsymmetric&nbsp;algorithm.</span></div></li>
<li><div class="src-line"><a name="a59"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">array&nbsp;</span></div></li>
<li><div class="src-line"><a name="a60"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a61"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$ort</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a62"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a63"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a64"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Used&nbsp;for&nbsp;complex&nbsp;scalar&nbsp;division.</span></div></li>
<li><div class="src-line"><a name="a65"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@var&nbsp;</span><span class="src-doc-type">float&nbsp;</span></div></li>
<li><div class="src-line"><a name="a66"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a67"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$cdivr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a68"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-var">$cdivi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a69"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a70"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a71"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a72"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Symmetric&nbsp;Householder&nbsp;reduction&nbsp;to&nbsp;tridiagonal&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a73"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a74"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;private</span></div></li>
<li><div class="src-line"><a name="a75"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a76"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-key">function&nbsp;</span><span class="src-id">tred2&nbsp;</span><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a77"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;&nbsp;This&nbsp;is&nbsp;derived&nbsp;from&nbsp;the&nbsp;Algol&nbsp;procedures&nbsp;tred2&nbsp;by</span></div></li>
<li><div class="src-line"><a name="a78"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;&nbsp;Bowdler,&nbsp;Martin,&nbsp;Reinsch,&nbsp;and&nbsp;Wilkinson,&nbsp;Handbook&nbsp;for</span></div></li>
<li><div class="src-line"><a name="a79"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;&nbsp;Auto.&nbsp;Comp.,&nbsp;Vol.ii-Linear&nbsp;Algebra,&nbsp;and&nbsp;the&nbsp;corresponding</span></div></li>
<li><div class="src-line"><a name="a80"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;&nbsp;Fortran&nbsp;subroutine&nbsp;in&nbsp;EISPACK.</span></div></li>
<li><div class="src-line"><a name="a81"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a82"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Householder&nbsp;reduction&nbsp;to&nbsp;tridiagonal&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a83"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&gt;&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a84"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$i_&nbsp;</span>=&nbsp;<span class="src-var">$i&nbsp;</span>-<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a85"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Scale&nbsp;to&nbsp;avoid&nbsp;under/overflow.</span></div></li>
<li><div class="src-line"><a name="a86"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>=&nbsp;<span class="src-var">$scale&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a87"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$scale&nbsp;</span>+=&nbsp;<a href="http://www.php.net/array_sum">array_sum</a><span class="src-sym">(</span><a href="http://www.php.net/array_map">array_map</a><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a88"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$scale&nbsp;</span>==&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a89"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i_</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a90"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d&nbsp;</span>=&nbsp;<a href="http://www.php.net/array_slice">array_slice</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i_</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-num">0</span><span class="src-sym">,&nbsp;</span><span class="src-var">$i_</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a91"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a92"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a93"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a94"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a95"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Generate&nbsp;Householder&nbsp;vector.</span></div></li>
<li><div class="src-line"><a name="a96"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a97"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>/=&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a98"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>+=&nbsp;<a href="http://www.php.net/pow">pow</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-num">2</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a99"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a100"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i_</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a101"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><span class="src-var">$h</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a102"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$f&nbsp;</span>&gt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a103"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;-<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a104"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a105"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$scale&nbsp;</span>*&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a106"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>=&nbsp;<span class="src-var">$h&nbsp;</span>-&nbsp;<span class="src-var">$f&nbsp;</span>*&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a107"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i_</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$f&nbsp;</span>-&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a108"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a109"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a110"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a111"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Apply&nbsp;similarity&nbsp;transformation&nbsp;to&nbsp;remaining&nbsp;columns.</span></div></li>
<li><div class="src-line"><a name="a112"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a113"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a114"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$f</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a115"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$f</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a116"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$j</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i_</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a117"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a118"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$f</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a119"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a120"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a121"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a122"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a123"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a124"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>/=&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a125"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a126"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a127"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$hh&nbsp;</span>=&nbsp;<span class="src-var">$f&nbsp;</span>/&nbsp;<span class="src-sym">(</span><span class="src-num">2&nbsp;</span>*&nbsp;<span class="src-var">$h</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a128"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j</span>=<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a129"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$hh&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a130"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a131"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a132"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a133"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a134"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$j</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i_</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a135"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-sym">(</span><span class="src-var">$f&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$g&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a136"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a137"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a138"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a139"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a140"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a141"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a142"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a143"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a144"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Accumulate&nbsp;transformations.</span></div></li>
<li><div class="src-line"><a name="a145"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a146"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a147"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a148"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a149"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$h&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a150"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a151"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a152"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a153"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a154"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a155"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a156"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a157"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a158"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a159"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$g&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a160"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a161"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a162"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a163"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a164"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a165"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a166"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a167"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a168"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a169"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<a href="http://www.php.net/array_fill">array_fill</a><span class="src-sym">(</span><span class="src-num">0</span><span class="src-sym">,&nbsp;</span><span class="src-var">$j</span><span class="src-sym">,&nbsp;</span><span class="src-num">0.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a170"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a171"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-num">0</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a172"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a173"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a174"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a175"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a176"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Symmetric&nbsp;tridiagonal&nbsp;QL&nbsp;algorithm.</span></div></li>
<li><div class="src-line"><a name="a177"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a178"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;This&nbsp;is&nbsp;derived&nbsp;from&nbsp;the&nbsp;Algol&nbsp;procedures&nbsp;tql2,&nbsp;by</span></div></li>
<li><div class="src-line"><a name="a179"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Bowdler,&nbsp;Martin,&nbsp;Reinsch,&nbsp;and&nbsp;Wilkinson,&nbsp;Handbook&nbsp;for</span></div></li>
<li><div class="src-line"><a name="a180"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Auto.&nbsp;Comp.,&nbsp;Vol.ii-Linear&nbsp;Algebra,&nbsp;and&nbsp;the&nbsp;corresponding</span></div></li>
<li><div class="src-line"><a name="a181"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Fortran&nbsp;subroutine&nbsp;in&nbsp;EISPACK.</span></div></li>
<li><div class="src-line"><a name="a182"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a183"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;private</span></div></li>
<li><div class="src-line"><a name="a184"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a185"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-key">function&nbsp;</span><span class="src-id">tql2</span><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a186"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a187"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a188"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a189"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a190"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a191"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$tst1&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a192"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$eps&nbsp;&nbsp;</span>=&nbsp;<a href="http://www.php.net/pow">pow</a><span class="src-sym">(</span><span class="src-num">2.0</span><span class="src-sym">,</span>-<span class="src-num">52.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a193"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a194"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$l&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$l&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$l</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a195"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Find&nbsp;small&nbsp;subdiagonal&nbsp;element</span></div></li>
<li><div class="src-line"><a name="a196"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$tst1&nbsp;</span>=&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><span class="src-var">$tst1</span><span class="src-sym">,&nbsp;</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a197"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$m&nbsp;</span>=&nbsp;<span class="src-var">$l</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a198"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">while&nbsp;</span><span class="src-sym">(</span><span class="src-var">$m&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a199"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>&lt;=&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$tst1</span><span class="src-sym">)</span></div></li>
<li><div class="src-line"><a name="a200"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a201"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;++<span class="src-var">$m</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a202"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a203"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;If&nbsp;m&nbsp;==&nbsp;l,&nbsp;$this-&gt;d[l]&nbsp;is&nbsp;an&nbsp;eigenvalue,</span></div></li>
<li><div class="src-line"><a name="a204"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;otherwise,&nbsp;iterate.</span></div></li>
<li><div class="src-line"><a name="a205"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$m&nbsp;</span>&gt;&nbsp;<span class="src-var">$l</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a206"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a207"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;do&nbsp;<span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a208"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Could&nbsp;check&nbsp;iteration&nbsp;count&nbsp;here.</span></div></li>
<li><div class="src-line"><a name="a209"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>+=&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a210"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;implicit&nbsp;shift</span></div></li>
<li><div class="src-line"><a name="a211"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a212"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$g</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-sym">(</span><span class="src-num">2.0&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a213"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$p</span><span class="src-sym">,&nbsp;</span><span class="src-num">1.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a214"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>&lt;&nbsp;<span class="src-num">0</span><span class="src-sym">)</span></div></li>
<li><div class="src-line"><a name="a215"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>*=&nbsp;-<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a216"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$r</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a217"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$r</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a218"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$dl1&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a219"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>=&nbsp;<span class="src-var">$g&nbsp;</span>-&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a220"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$l&nbsp;</span>+&nbsp;<span class="src-num">2</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)</span></div></li>
<li><div class="src-line"><a name="a221"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a222"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>+=&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a223"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Implicit&nbsp;QL&nbsp;transformation.</span></div></li>
<li><div class="src-line"><a name="a224"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a225"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$c&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a226"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$c2&nbsp;</span>=&nbsp;<span class="src-var">$c3&nbsp;</span>=&nbsp;<span class="src-var">$c</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a227"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$el1&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a228"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$s2&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a229"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&gt;=&nbsp;<span class="src-var">$l</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a230"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$c3&nbsp;</span>=&nbsp;<span class="src-var">$c2</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a231"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$c2&nbsp;</span>=&nbsp;<span class="src-var">$c</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a232"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s2&nbsp;</span>=&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a233"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a234"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a235"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;&nbsp;</span>=&nbsp;<a href="../JAMA/_PHPExcel---Shared---JAMA---utils---Maths.php.html#functionhypo">hypo</a><span class="src-sym">(</span><span class="src-var">$p</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a236"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a237"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a238"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$c&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>/&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a239"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a240"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$h&nbsp;</span>+&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$g&nbsp;</span>+&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a241"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Accumulate&nbsp;transformation.</span></div></li>
<li><div class="src-line"><a name="a242"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a243"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a244"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a245"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a246"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a247"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a248"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;-<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$s2&nbsp;</span>*&nbsp;<span class="src-var">$c3&nbsp;</span>*&nbsp;<span class="src-var">$el1&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$dl1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a249"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a250"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$c&nbsp;</span>*&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a251"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Check&nbsp;for&nbsp;convergence.</span></div></li>
<li><div class="src-line"><a name="a252"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">while&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>&gt;&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$tst1</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a253"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a254"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$f</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a255"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a256"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a257"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a258"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Sort&nbsp;eigenvalues&nbsp;and&nbsp;corresponding&nbsp;vectors.</span></div></li>
<li><div class="src-line"><a name="a259"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a260"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$i</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a261"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a262"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a263"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a264"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$j</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a265"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a266"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a267"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a268"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>!=&nbsp;<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a269"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a270"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a271"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a272"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a273"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a274"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a275"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a276"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a277"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a278"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a279"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a280"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a281"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a282"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Nonsymmetric&nbsp;reduction&nbsp;to&nbsp;Hessenberg&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a283"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a284"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;This&nbsp;is&nbsp;derived&nbsp;from&nbsp;the&nbsp;Algol&nbsp;procedures&nbsp;orthes&nbsp;and&nbsp;ortran,</span></div></li>
<li><div class="src-line"><a name="a285"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;by&nbsp;Martin&nbsp;and&nbsp;Wilkinson,&nbsp;Handbook&nbsp;for&nbsp;Auto.&nbsp;Comp.,</span></div></li>
<li><div class="src-line"><a name="a286"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Vol.ii-Linear&nbsp;Algebra,&nbsp;and&nbsp;the&nbsp;corresponding</span></div></li>
<li><div class="src-line"><a name="a287"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Fortran&nbsp;subroutines&nbsp;in&nbsp;EISPACK.</span></div></li>
<li><div class="src-line"><a name="a288"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a289"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;private</span></div></li>
<li><div class="src-line"><a name="a290"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a291"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-key">function&nbsp;</span><span class="src-id">orthes&nbsp;</span><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a292"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$low&nbsp;&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a293"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$high&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span>-<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a294"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a295"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$m&nbsp;</span>=&nbsp;<span class="src-var">$low</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$m&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$m</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a296"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Scale&nbsp;column.</span></div></li>
<li><div class="src-line"><a name="a297"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$scale&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a298"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a299"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$scale&nbsp;</span>=&nbsp;<span class="src-var">$scale&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a300"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a301"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$scale&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a302"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Compute&nbsp;Householder&nbsp;transformation.</span></div></li>
<li><div class="src-line"><a name="a303"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a304"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&gt;=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a305"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$scale</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a306"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a307"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a308"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><span class="src-var">$h</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a309"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]&nbsp;</span>&gt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a310"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>*=&nbsp;-<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a311"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a312"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$h&nbsp;</span>-=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a313"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a314"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Apply&nbsp;Householder&nbsp;similarity&nbsp;transformation</span></div></li>
<li><div class="src-line"><a name="a315"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;H&nbsp;=&nbsp;(I&nbsp;-u&nbsp;*&nbsp;u'&nbsp;/&nbsp;h)&nbsp;*&nbsp;H&nbsp;*&nbsp;(I&nbsp;-u&nbsp;*&nbsp;u')&nbsp;/&nbsp;h)</span></div></li>
<li><div class="src-line"><a name="a316"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a317"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a318"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&gt;=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a319"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a320"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a321"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>/=&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a322"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a323"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$f&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a324"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a325"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a326"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a327"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a328"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&gt;=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a329"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a330"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a331"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$f&nbsp;</span>=&nbsp;<span class="src-var">$f&nbsp;</span>/&nbsp;<span class="src-var">$h</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a332"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a333"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$f&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a334"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a335"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a336"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$scale&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a337"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$scale&nbsp;</span>*&nbsp;<span class="src-var">$g</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a338"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a339"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a340"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a341"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Accumulate&nbsp;transformations&nbsp;(Algol's&nbsp;ortran).</span></div></li>
<li><div class="src-line"><a name="a342"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a343"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a344"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>==&nbsp;<span class="src-var">$j&nbsp;</span>?&nbsp;<span class="src-num">1.0&nbsp;</span>:&nbsp;<span class="src-num">0.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a345"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a346"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a347"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$m&nbsp;</span>=&nbsp;<span class="src-var">$high</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$m&nbsp;</span>&gt;=&nbsp;<span class="src-var">$low</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$m</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a348"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a349"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a350"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a351"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a352"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a353"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a354"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a355"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>+=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a356"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a357"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Double&nbsp;division&nbsp;avoids&nbsp;possible&nbsp;underflow</span></div></li>
<li><div class="src-line"><a name="a358"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$g&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$g&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a359"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a360"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+=&nbsp;<span class="src-var">$g&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a361"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a362"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a363"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a364"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a365"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a366"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a367"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a368"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a369"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Performs&nbsp;complex&nbsp;division.</span></div></li>
<li><div class="src-line"><a name="a370"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a371"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;private</span></div></li>
<li><div class="src-line"><a name="a372"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a373"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-key">function&nbsp;</span><span class="src-id">cdiv</span><span class="src-sym">(</span><span class="src-var">$xr</span><span class="src-sym">,&nbsp;</span><span class="src-var">$xi</span><span class="src-sym">,&nbsp;</span><span class="src-var">$yr</span><span class="src-sym">,&nbsp;</span><span class="src-var">$yi</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a374"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$yr</span><span class="src-sym">)&nbsp;</span>&gt;&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$yi</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a375"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$yi&nbsp;</span>/&nbsp;<span class="src-var">$yr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a376"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$d&nbsp;</span>=&nbsp;<span class="src-var">$yr&nbsp;</span>+&nbsp;<span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$yi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a377"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivr&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$xr&nbsp;</span>+&nbsp;<span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$xi</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$d</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a378"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivi&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$xi&nbsp;</span>-&nbsp;<span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$xr</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$d</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a379"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a380"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$yr&nbsp;</span>/&nbsp;<span class="src-var">$yi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a381"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$d&nbsp;</span>=&nbsp;<span class="src-var">$yi&nbsp;</span>+&nbsp;<span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$yr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a382"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivr&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$xr&nbsp;</span>+&nbsp;<span class="src-var">$xi</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$d</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a383"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivi&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$xi&nbsp;</span>-&nbsp;<span class="src-var">$xr</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$d</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a384"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a385"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a386"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a387"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a388"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a389"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Nonsymmetric&nbsp;reduction&nbsp;from&nbsp;Hessenberg&nbsp;to&nbsp;real&nbsp;Schur&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a390"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a391"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Code&nbsp;is&nbsp;derived&nbsp;from&nbsp;the&nbsp;Algol&nbsp;procedure&nbsp;hqr2,</span></div></li>
<li><div class="src-line"><a name="a392"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;by&nbsp;Martin&nbsp;and&nbsp;Wilkinson,&nbsp;Handbook&nbsp;for&nbsp;Auto.&nbsp;Comp.,</span></div></li>
<li><div class="src-line"><a name="a393"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Vol.ii-Linear&nbsp;Algebra,&nbsp;and&nbsp;the&nbsp;corresponding</span></div></li>
<li><div class="src-line"><a name="a394"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Fortran&nbsp;subroutine&nbsp;in&nbsp;EISPACK.</span></div></li>
<li><div class="src-line"><a name="a395"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a396"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;private</span></div></li>
<li><div class="src-line"><a name="a397"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a398"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">private&nbsp;</span><span class="src-key">function&nbsp;</span><span class="src-id">hqr2&nbsp;</span><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a399"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;&nbsp;Initialize</span></div></li>
<li><div class="src-line"><a name="a400"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$nn&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a401"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$n&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$nn&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a402"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$low&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a403"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$high&nbsp;</span>=&nbsp;<span class="src-var">$nn&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a404"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$eps&nbsp;</span>=&nbsp;<a href="http://www.php.net/pow">pow</a><span class="src-sym">(</span><span class="src-num">2.0</span><span class="src-sym">,&nbsp;</span>-<span class="src-num">52.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a405"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$exshift&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a406"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a407"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Store&nbsp;roots&nbsp;isolated&nbsp;by&nbsp;balanc&nbsp;and&nbsp;compute&nbsp;matrix&nbsp;norm</span></div></li>
<li><div class="src-line"><a name="a408"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$norm&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a409"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a410"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$nn</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a411"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$low</span><span class="src-sym">)&nbsp;</span><span class="src-key">OR&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>&gt;&nbsp;<span class="src-var">$high</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a412"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a413"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a414"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a415"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><span class="src-var">$i</span>-<span class="src-num">1</span><span class="src-sym">,&nbsp;</span><span class="src-num">0</span><span class="src-sym">)</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nn</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a416"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$norm&nbsp;</span>=&nbsp;<span class="src-var">$norm&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a417"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a418"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a419"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a420"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Outer&nbsp;loop&nbsp;over&nbsp;eigenvalue&nbsp;index</span></div></li>
<li><div class="src-line"><a name="a421"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a422"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">while&nbsp;</span><span class="src-sym">(</span><span class="src-var">$n&nbsp;</span>&gt;=&nbsp;<span class="src-var">$low</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a423"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Look&nbsp;for&nbsp;single&nbsp;small&nbsp;sub-diagonal&nbsp;element</span></div></li>
<li><div class="src-line"><a name="a424"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$l&nbsp;</span>=&nbsp;<span class="src-var">$n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a425"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">while&nbsp;</span><span class="src-sym">(</span><span class="src-var">$l&nbsp;</span>&gt;&nbsp;<span class="src-var">$low</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a426"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$l</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$l</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a427"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$s&nbsp;</span>==&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a428"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$norm</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a429"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a430"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$l</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$l</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>&lt;&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$s</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a431"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a432"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a433"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;--<span class="src-var">$l</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a434"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a435"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Check&nbsp;for&nbsp;convergence</span></div></li>
<li><div class="src-line"><a name="a436"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;One&nbsp;root&nbsp;found</span></div></li>
<li><div class="src-line"><a name="a437"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$l&nbsp;</span>==&nbsp;<span class="src-var">$n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a438"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$exshift</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a439"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a440"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a441"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;--<span class="src-var">$n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a442"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a443"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Two&nbsp;roots&nbsp;found</span></div></li>
<li><div class="src-line"><a name="a444"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$l&nbsp;</span>==&nbsp;<span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a445"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a446"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-num">2.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a447"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$w</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a448"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$q</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a449"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$exshift</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a450"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$exshift</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a451"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a452"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Real&nbsp;pair</span></div></li>
<li><div class="src-line"><a name="a453"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$q&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a454"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a455"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a456"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a457"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>-&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a458"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a459"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>+&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a460"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a461"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$z&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a462"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>-&nbsp;<span class="src-var">$w&nbsp;</span>/&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a463"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a464"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a465"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a466"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a467"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$x</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$z</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a468"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a469"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$z&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a470"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$q</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a471"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>/&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a472"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>/&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a473"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Row&nbsp;modification</span></div></li>
<li><div class="src-line"><a name="a474"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nn</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a475"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a476"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$z&nbsp;</span>+&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a477"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a478"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a479"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Column&nbsp;modification</span></div></li>
<li><div class="src-line"><a name="a480"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-id">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a481"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a482"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$z&nbsp;</span>+&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a483"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a484"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a485"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Accumulate&nbsp;transformations</span></div></li>
<li><div class="src-line"><a name="a486"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a487"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a488"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$z&nbsp;</span>+&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a489"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a490"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a491"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Complex&nbsp;pair</span></div></li>
<li><div class="src-line"><a name="a492"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a493"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>+&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a494"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>+&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a495"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a496"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a497"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a498"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$n&nbsp;</span>=&nbsp;<span class="src-var">$n&nbsp;</span>-&nbsp;<span class="src-num">2</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a499"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a500"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;No&nbsp;convergence&nbsp;yet</span></div></li>
<li><div class="src-line"><a name="a501"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a502"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Form&nbsp;shift</span></div></li>
<li><div class="src-line"><a name="a503"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a504"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a505"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a506"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$l&nbsp;</span>&lt;&nbsp;<span class="src-var">$n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a507"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a508"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a509"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a510"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Wilkinson's&nbsp;original&nbsp;ad&nbsp;hoc&nbsp;shift</span></div></li>
<li><div class="src-line"><a name="a511"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$iter&nbsp;</span>==&nbsp;<span class="src-num">10</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a512"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$exshift&nbsp;</span>+=&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a513"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a514"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a515"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a516"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a517"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-num">0.75&nbsp;</span>*&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a518"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;-<span class="src-num">0.4375&nbsp;</span>*&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a519"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a520"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;MATLAB's&nbsp;new&nbsp;ad&nbsp;hoc&nbsp;shift</span></div></li>
<li><div class="src-line"><a name="a521"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$iter&nbsp;</span>==&nbsp;<span class="src-num">30</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a522"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$y&nbsp;</span>-&nbsp;<span class="src-var">$x</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-num">2.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a523"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$s&nbsp;</span>+&nbsp;<span class="src-var">$w</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a524"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$s&nbsp;</span>&gt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a525"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><span class="src-var">$s</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a526"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$y&nbsp;</span>&lt;&nbsp;<span class="src-var">$x</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a527"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;-<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a528"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a529"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>-&nbsp;<span class="src-var">$w&nbsp;</span>/&nbsp;<span class="src-sym">((</span><span class="src-var">$y&nbsp;</span>-&nbsp;<span class="src-var">$x</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-num">2.0&nbsp;</span>+&nbsp;<span class="src-var">$s</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a530"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a531"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-=&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a532"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a533"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$exshift&nbsp;</span>+=&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a534"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;<span class="src-num">0.964</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a535"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a536"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a537"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Could&nbsp;check&nbsp;iteration&nbsp;count&nbsp;here.</span></div></li>
<li><div class="src-line"><a name="a538"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$iter&nbsp;</span>=&nbsp;<span class="src-var">$iter&nbsp;</span>+&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a539"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Look&nbsp;for&nbsp;two&nbsp;consecutive&nbsp;small&nbsp;sub-diagonal&nbsp;elements</span></div></li>
<li><div class="src-line"><a name="a540"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$m&nbsp;</span>=&nbsp;<span class="src-var">$n&nbsp;</span>-&nbsp;<span class="src-num">2</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a541"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">while&nbsp;</span><span class="src-sym">(</span><span class="src-var">$m&nbsp;</span>&gt;=&nbsp;<span class="src-var">$l</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a542"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a543"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>-&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a544"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$y&nbsp;</span>-&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a545"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$s&nbsp;</span>-&nbsp;<span class="src-var">$w</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a546"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$z&nbsp;</span>-&nbsp;<span class="src-var">$r&nbsp;</span>-&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a547"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a548"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$q</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$r</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a549"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a550"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a551"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$r&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a552"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$m&nbsp;</span>==&nbsp;<span class="src-var">$l</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a553"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a554"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a555"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$q</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$r</span><span class="src-sym">))&nbsp;</span>&lt;</div></li>
<li><div class="src-line"><a name="a556"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$z</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$m</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">))))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a557"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a558"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a559"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;--<span class="src-var">$m</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a560"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a561"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$m&nbsp;</span>+&nbsp;<span class="src-num">2</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a562"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>-<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a563"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>&gt;&nbsp;<span class="src-var">$m</span>+<span class="src-num">2</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a564"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>-<span class="src-num">3</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a565"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a566"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a567"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Double&nbsp;QR&nbsp;step&nbsp;involving&nbsp;rows&nbsp;l:n&nbsp;and&nbsp;columns&nbsp;m:n</span></div></li>
<li><div class="src-line"><a name="a568"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$m</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a569"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$notlast&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>!=&nbsp;<span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a570"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>!=&nbsp;<span class="src-var">$m</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a571"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a572"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a573"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$notlast&nbsp;</span>?&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>:&nbsp;<span class="src-num">0.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a574"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$q</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$r</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a575"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$x&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a576"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>/&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a577"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>/&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a578"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$r&nbsp;</span>/&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a579"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a580"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a581"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$x&nbsp;</span>==&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a582"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">break</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a583"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a584"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<a href="http://www.php.net/sqrt">sqrt</a><span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$q&nbsp;</span>+&nbsp;<span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$r</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a585"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$p&nbsp;</span>&lt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a586"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;-<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a587"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a588"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$s&nbsp;</span>!=&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a589"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>!=&nbsp;<span class="src-var">$m</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a590"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$s&nbsp;</span>*&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a591"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">elseif&nbsp;</span><span class="src-sym">(</span><span class="src-var">$l&nbsp;</span>!=&nbsp;<span class="src-var">$m</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a592"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a593"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a594"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a595"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a596"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a597"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$r&nbsp;</span>/&nbsp;<span class="src-var">$s</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a598"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>/&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a599"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$r&nbsp;</span>/&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a600"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Row&nbsp;modification</span></div></li>
<li><div class="src-line"><a name="a601"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$k</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nn</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a602"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a603"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$notlast</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a604"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$r&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a605"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a606"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a607"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a608"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$y</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a609"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a610"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Column&nbsp;modification</span></div></li>
<li><div class="src-line"><a name="a611"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$n</span><span class="src-sym">,&nbsp;</span><span class="src-var">$k</span>+<span class="src-num">3</span><span class="src-sym">)</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a612"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$y&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a613"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$notlast</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a614"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$z&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a615"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a616"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a617"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a618"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$q</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a619"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a620"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Accumulate&nbsp;transformations</span></div></li>
<li><div class="src-line"><a name="a621"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a622"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$x&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$y&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a623"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$notlast</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a624"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$p&nbsp;</span>+&nbsp;<span class="src-var">$z&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a625"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">2</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a626"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a627"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a628"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span>+<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p&nbsp;</span>*&nbsp;<span class="src-var">$q</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a629"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a630"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;($s&nbsp;!=&nbsp;0)</span></div></li>
<li><div class="src-line"><a name="a631"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;k&nbsp;loop</span></div></li>
<li><div class="src-line"><a name="a632"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;check&nbsp;convergence</span></div></li>
<li><div class="src-line"><a name="a633"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;while&nbsp;($n&nbsp;&gt;=&nbsp;$low)</span></div></li>
<li><div class="src-line"><a name="a634"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a635"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Backsubstitute&nbsp;to&nbsp;find&nbsp;vectors&nbsp;of&nbsp;upper&nbsp;triangular&nbsp;form</span></div></li>
<li><div class="src-line"><a name="a636"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$norm&nbsp;</span>==&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a637"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a638"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a639"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a640"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$n&nbsp;</span>=&nbsp;<span class="src-var">$nn</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$n&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a641"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$p&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a642"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a643"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Real&nbsp;vector</span></div></li>
<li><div class="src-line"><a name="a644"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$q&nbsp;</span>==&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a645"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$l&nbsp;</span>=&nbsp;<span class="src-var">$n</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a646"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a647"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a648"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a649"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a650"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$l</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a651"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$r&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a652"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a653"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a654"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$w</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a655"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$r</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a656"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a657"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$l&nbsp;</span>=&nbsp;<span class="src-var">$i</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a658"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>==&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a659"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$w&nbsp;</span>!=&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a660"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$r&nbsp;</span>/&nbsp;<span class="src-var">$w</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a661"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a662"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-var">$r&nbsp;</span>/&nbsp;<span class="src-sym">(</span><span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$norm</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a663"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a664"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Solve&nbsp;real&nbsp;equations</span></div></li>
<li><div class="src-line"><a name="a665"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a666"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a667"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a668"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$q&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a669"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$x&nbsp;</span>*&nbsp;<span class="src-var">$s&nbsp;</span>-&nbsp;<span class="src-var">$z&nbsp;</span>*&nbsp;<span class="src-var">$r</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$q</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a670"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a671"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$x</span><span class="src-sym">)&nbsp;</span>&gt;&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$z</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a672"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-sym">(</span>-<span class="src-var">$r&nbsp;</span>-&nbsp;<span class="src-var">$w&nbsp;</span>*&nbsp;<span class="src-var">$t</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a673"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a674"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-sym">(</span>-<span class="src-var">$s&nbsp;</span>-&nbsp;<span class="src-var">$y&nbsp;</span>*&nbsp;<span class="src-var">$t</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a675"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a676"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a677"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Overflow&nbsp;control</span></div></li>
<li><div class="src-line"><a name="a678"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a679"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$t</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-var">$t&nbsp;</span>&gt;&nbsp;<span class="src-num">1</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a680"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a681"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a682"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a683"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a684"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a685"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a686"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Complex&nbsp;vector</span></div></li>
<li><div class="src-line"><a name="a687"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$q&nbsp;</span>&lt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a688"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$l&nbsp;</span>=&nbsp;<span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a689"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Last&nbsp;vector&nbsp;component&nbsp;imaginary&nbsp;so&nbsp;matrix&nbsp;is&nbsp;triangular</span></div></li>
<li><div class="src-line"><a name="a690"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>&gt;&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a691"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$q&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a692"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;-<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a693"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a694"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">cdiv</span><span class="src-sym">(</span><span class="src-num">0.0</span><span class="src-sym">,&nbsp;</span>-<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">,&nbsp;</span><span class="src-var">$q</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a695"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a696"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a697"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a698"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a699"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-num">1.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a700"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$n</span>-<span class="src-num">2</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&gt;=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a701"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;double&nbsp;ra,sa,vr,vi;</span></div></li>
<li><div class="src-line"><a name="a702"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$ra&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a703"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sa&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a704"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$l</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a705"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$ra&nbsp;</span>=&nbsp;<span class="src-var">$ra&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a706"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$sa&nbsp;</span>=&nbsp;<span class="src-var">$sa&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a707"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a708"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$w&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a709"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>&lt;&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a710"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$w</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a711"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$r&nbsp;</span>=&nbsp;<span class="src-var">$ra</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a712"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$s&nbsp;</span>=&nbsp;<span class="src-var">$sa</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a713"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a714"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$l&nbsp;</span>=&nbsp;<span class="src-var">$i</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a715"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>==&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a716"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">cdiv</span><span class="src-sym">(</span>-<span class="src-var">$ra</span><span class="src-sym">,&nbsp;</span>-<span class="src-var">$sa</span><span class="src-sym">,&nbsp;</span><span class="src-var">$w</span><span class="src-sym">,&nbsp;</span><span class="src-var">$q</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a717"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a718"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a719"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a720"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Solve&nbsp;complex&nbsp;equations</span></div></li>
<li><div class="src-line"><a name="a721"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$x&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a722"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$y&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a723"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$vr&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$q</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a724"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$vi&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$p</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-num">2.0&nbsp;</span>*&nbsp;<span class="src-var">$q</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a725"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$vr&nbsp;</span>==&nbsp;<span class="src-num">0.0&nbsp;</span><span class="src-sym">&amp;&nbsp;</span><span class="src-var">$vi&nbsp;</span>==&nbsp;<span class="src-num">0.0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a726"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$vr&nbsp;</span>=&nbsp;<span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$norm&nbsp;</span>*&nbsp;<span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$w</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$q</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$x</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$y</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$z</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a727"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a728"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">cdiv</span><span class="src-sym">(</span><span class="src-var">$x&nbsp;</span>*&nbsp;<span class="src-var">$r&nbsp;</span>-&nbsp;<span class="src-var">$z&nbsp;</span>*&nbsp;<span class="src-var">$ra&nbsp;</span>+&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$sa</span><span class="src-sym">,&nbsp;</span><span class="src-var">$x&nbsp;</span>*&nbsp;<span class="src-var">$s&nbsp;</span>-&nbsp;<span class="src-var">$z&nbsp;</span>*&nbsp;<span class="src-var">$sa&nbsp;</span>-&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$ra</span><span class="src-sym">,&nbsp;</span><span class="src-var">$vr</span><span class="src-sym">,&nbsp;</span><span class="src-var">$vi</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a729"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a730"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a731"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$x</span><span class="src-sym">)&nbsp;</span>&gt;&nbsp;<span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$z</span><span class="src-sym">)&nbsp;</span>+&nbsp;<a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$q</span><span class="src-sym">)))&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a732"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-sym">(</span>-<span class="src-var">$ra&nbsp;</span>-&nbsp;<span class="src-var">$w&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>+&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a733"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-sym">(</span>-<span class="src-var">$sa&nbsp;</span>-&nbsp;<span class="src-var">$w&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>-&nbsp;<span class="src-var">$q&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)&nbsp;</span>/&nbsp;<span class="src-var">$x</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a734"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a735"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">cdiv</span><span class="src-sym">(</span>-<span class="src-var">$r&nbsp;</span>-&nbsp;<span class="src-var">$y&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span>-<span class="src-var">$s&nbsp;</span>-&nbsp;<span class="src-var">$y&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">,&nbsp;</span><span class="src-var">$z</span><span class="src-sym">,&nbsp;</span><span class="src-var">$q</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a736"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivr</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a737"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span>+<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">cdivi</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a738"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a739"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a740"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Overflow&nbsp;control</span></div></li>
<li><div class="src-line"><a name="a741"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$t&nbsp;</span>=&nbsp;<a href="http://www.php.net/max">max</a><span class="src-sym">(</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">,</span><a href="http://www.php.net/abs">abs</a><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]</span><span class="src-sym">))</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a742"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">((</span><span class="src-var">$eps&nbsp;</span>*&nbsp;<span class="src-var">$t</span><span class="src-sym">)&nbsp;</span>*&nbsp;<span class="src-var">$t&nbsp;</span>&gt;&nbsp;<span class="src-num">1</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a743"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;=&nbsp;<span class="src-var">$n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a744"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span>-<span class="src-num">1</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a745"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;&nbsp;&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$n</span><span class="src-sym">]&nbsp;</span>/&nbsp;<span class="src-var">$t</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a746"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a747"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a748"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;else</span></div></li>
<li><div class="src-line"><a name="a749"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;for</span></div></li>
<li><div class="src-line"><a name="a750"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;else&nbsp;for&nbsp;complex&nbsp;case</span></div></li>
<li><div class="src-line"><a name="a751"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;for</span></div></li>
<li><div class="src-line"><a name="a752"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a753"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Vectors&nbsp;of&nbsp;isolated&nbsp;roots</span></div></li>
<li><div class="src-line"><a name="a754"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$nn</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a755"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$low&nbsp;</span>|&nbsp;<span class="src-var">$i&nbsp;</span>&gt;&nbsp;<span class="src-var">$high</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a756"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$i</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$nn</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a757"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a758"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a759"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a760"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a761"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a762"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Back&nbsp;transformation&nbsp;to&nbsp;get&nbsp;eigenvectors&nbsp;of&nbsp;original&nbsp;matrix</span></div></li>
<li><div class="src-line"><a name="a763"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-var">$nn</span>-<span class="src-num">1</span><span class="src-sym">;&nbsp;</span><span class="src-var">$j&nbsp;</span>&gt;=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span>--<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a764"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;=&nbsp;<span class="src-var">$high</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a765"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-num">0.0</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a766"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$k&nbsp;</span>=&nbsp;<span class="src-var">$low</span><span class="src-sym">;&nbsp;</span><span class="src-var">$k&nbsp;</span>&lt;=&nbsp;<a href="http://www.php.net/min">min</a><span class="src-sym">(</span><span class="src-var">$j</span><span class="src-sym">,</span><span class="src-var">$high</span><span class="src-sym">)</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$k</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a767"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$z&nbsp;</span>=&nbsp;<span class="src-var">$z&nbsp;</span>+&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]&nbsp;</span>*&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H</span><span class="src-sym">[</span><span class="src-var">$k</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a768"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a769"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$z</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a770"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a771"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a772"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-comm">//&nbsp;end&nbsp;hqr2</span></div></li>
<li><div class="src-line"><a name="a773"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a774"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a775"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a776"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Constructor:&nbsp;Check&nbsp;for&nbsp;symmetry,&nbsp;then&nbsp;construct&nbsp;the&nbsp;eigenvalue&nbsp;decomposition</span></div></li>
<li><div class="src-line"><a name="a777"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a778"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a779"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@param&nbsp;</span><span class="src-doc-type">A&nbsp;</span><span class="src-doc">&nbsp;Square&nbsp;matrix</span></div></li>
<li><div class="src-line"><a name="a780"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">Structure&nbsp;</span><span class="src-doc">to&nbsp;access&nbsp;D&nbsp;and&nbsp;V.</span></div></li>
<li><div class="src-line"><a name="a781"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a782"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/EigenvalueDecomposition.html#method__construct">__construct</a><span class="src-sym">(</span><span class="src-var">$Arg</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a783"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">A&nbsp;</span>=&nbsp;<span class="src-var">$Arg</span><span class="src-sym">-&gt;</span><span class="src-id">getArray</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a784"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n&nbsp;</span>=&nbsp;<span class="src-var">$Arg</span><span class="src-sym">-&gt;</span><span class="src-id">getColumnDimension</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a785"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a786"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$issymmetric&nbsp;</span>=&nbsp;<span class="src-id">true</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a787"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-sym">(</span><span class="src-var">$j&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">&amp;&nbsp;</span><span class="src-var">$issymmetric</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$j</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a788"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)&nbsp;</span><span class="src-sym">&amp;&nbsp;</span><span class="src-var">$issymmetric</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a789"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$issymmetric&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">A</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]&nbsp;</span>==&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">A</span><span class="src-sym">[</span><span class="src-var">$j</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a790"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a791"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a792"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a793"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$issymmetric</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a794"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">A</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a795"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Tridiagonalize.</span></div></li>
<li><div class="src-line"><a name="a796"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">tred2</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a797"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Diagonalize.</span></div></li>
<li><div class="src-line"><a name="a798"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">tql2</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a799"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}&nbsp;</span><span class="src-key">else&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a800"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">H&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">A</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a801"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">ort&nbsp;</span>=&nbsp;<span class="src-key">array</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a802"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Reduce&nbsp;to&nbsp;Hessenberg&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a803"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">orthes</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a804"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-comm">//&nbsp;Reduce&nbsp;Hessenberg&nbsp;to&nbsp;real&nbsp;Schur&nbsp;form.</span></div></li>
<li><div class="src-line"><a name="a805"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-id">hqr2</span><span class="src-sym">(</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a806"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a807"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a808"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a809"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a810"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a811"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;eigenvector&nbsp;matrix</span></div></li>
<li><div class="src-line"><a name="a812"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a813"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a814"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">V&nbsp;</span></div></li>
<li><div class="src-line"><a name="a815"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a816"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/EigenvalueDecomposition.html#methodgetV">getV</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a817"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id">Matrix</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">V</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a818"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a819"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a820"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a821"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a822"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;real&nbsp;parts&nbsp;of&nbsp;the&nbsp;eigenvalues</span></div></li>
<li><div class="src-line"><a name="a823"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a824"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a825"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">real(diag(D))&nbsp;</span></div></li>
<li><div class="src-line"><a name="a826"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a827"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/EigenvalueDecomposition.html#methodgetRealEigenvalues">getRealEigenvalues</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a828"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a829"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a830"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a831"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a832"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a833"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;imaginary&nbsp;parts&nbsp;of&nbsp;the&nbsp;eigenvalues</span></div></li>
<li><div class="src-line"><a name="a834"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a835"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a836"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">imag(diag(D))&nbsp;</span></div></li>
<li><div class="src-line"><a name="a837"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a838"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/EigenvalueDecomposition.html#methodgetImagEigenvalues">getImagEigenvalues</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a839"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a840"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a841"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a842"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a843"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-doc">/**</span></div></li>
<li><div class="src-line"><a name="a844"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;Return&nbsp;the&nbsp;block&nbsp;diagonal&nbsp;eigenvalue&nbsp;matrix</span></div></li>
<li><div class="src-line"><a name="a845"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*</span></div></li>
<li><div class="src-line"><a name="a846"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@access</span><span class="src-doc">&nbsp;public</span></div></li>
<li><div class="src-line"><a name="a847"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-doc-coretag">@return&nbsp;</span><span class="src-doc-type">D&nbsp;</span></div></li>
<li><div class="src-line"><a name="a848"></a><span class="src-doc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;*/</span></div></li>
<li><div class="src-line"><a name="a849"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">public&nbsp;</span><span class="src-key">function&nbsp;</span><a href="../JAMA/EigenvalueDecomposition.html#methodgetD">getD</a><span class="src-sym">(</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a850"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">for&nbsp;</span><span class="src-sym">(</span><span class="src-var">$i&nbsp;</span>=&nbsp;<span class="src-num">0</span><span class="src-sym">;&nbsp;</span><span class="src-var">$i&nbsp;</span>&lt;&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">;&nbsp;</span>++<span class="src-var">$i</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a851"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$D</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<a href="http://www.php.net/array_fill">array_fill</a><span class="src-sym">(</span><span class="src-num">0</span><span class="src-sym">,&nbsp;</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">n</span><span class="src-sym">,&nbsp;</span><span class="src-num">0.0</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a852"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$D</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">d</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a853"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">if&nbsp;</span><span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>==&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span><span class="src-sym">{</span></div></li>
<li><div class="src-line"><a name="a854"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">continue</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a855"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a856"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$o&nbsp;</span>=&nbsp;<span class="src-sym">(</span><span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]&nbsp;</span>&gt;&nbsp;<span class="src-num">0</span><span class="src-sym">)&nbsp;</span>?&nbsp;<span class="src-var">$i&nbsp;</span>+&nbsp;<span class="src-num">1&nbsp;</span>:&nbsp;<span class="src-var">$i&nbsp;</span>-&nbsp;<span class="src-num">1</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a857"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-var">$D</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">[</span><span class="src-var">$o</span><span class="src-sym">]&nbsp;</span>=&nbsp;<span class="src-var">$this</span><span class="src-sym">-&gt;</span><span class="src-var">e</span><span class="src-sym">[</span><span class="src-var">$i</span><span class="src-sym">]</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a858"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a859"></a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-key">return&nbsp;</span><span class="src-key">new&nbsp;</span><span class="src-id">Matrix</span><span class="src-sym">(</span><span class="src-var">$D</span><span class="src-sym">)</span><span class="src-sym">;</span></div></li>
<li><div class="src-line"><a name="a860"></a>&nbsp;&nbsp;&nbsp;&nbsp;<span class="src-sym">}</span></div></li>
<li><div class="src-line"><a name="a861"></a>&nbsp;</div></li>
<li><div class="src-line"><a name="a862"></a><span class="src-sym">}&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="src-comm">//&nbsp;&nbsp;&nbsp;&nbsp;class&nbsp;EigenvalueDecomposition</span></div></li>
</ol>
</div>
        <div class="credit">
		    <hr />
		    Documentation generated on Fri, 12 Oct 2012 00:16:09 +0200 by <a href="http://www.phpdoc.org">phpDocumentor 1.4.4</a>
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